Ads
related to: maximal matching formula in excel
Search results
Results From The WOW.Com Content Network
Maximum cardinality matching is a fundamental problem in graph theory. [1] We are given a graph G, and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this ...
A maximum matching (also known as maximum-cardinality matching [2]) is a matching that contains the largest possible number of edges. There may be many maximum matchings. The matching number of a graph G is the size of a maximum matching. Every maximum matching is maximal, but not every maximal matching is a maximum matching.
In the mathematical discipline of graph theory the Tutte–Berge formula is a characterization of the size of a maximum matching in a graph. It is a generalization of Tutte theorem on perfect matchings , and is named after W. T. Tutte (who proved Tutte's theorem) and Claude Berge (who proved its generalization).
Maximum independent set [3]: GT20 Maximum Induced path [3]: GT23 Minimum maximal independent set a.k.a. minimum independent dominating set [4] NP-complete special cases include the minimum maximal matching problem, [3]: GT10 which is essentially equal to the edge dominating set problem (see above). Metric dimension of a graph [3]: GT61
There is also a constant s which is at most the cardinality of a maximum matching in the graph. The goal is to find a minimum-cost matching of size exactly s. The most common case is the case in which the graph admits a one-sided-perfect matching (i.e., a matching of size r), and s=r. Unbalanced assignment can be reduced to a balanced assignment.
Given a bipartite graph G = (A ∪ B, E), the goal is to find the maximum cardinality matching in G that has minimum cost. Let w: E → R be a weight function on the edges of E. The minimum weight bipartite matching problem or assignment problem is to find a perfect matching M ⊆ E whose total weight is minimized. The idea is to reduce this ...
A matching in G is a subset M of E, such that each vertex in V is adjacent to at most a single edge in M. A maximum matching is a matching of maximum cardinality. An edge e in E is called maximally matchable (or allowed) if there exists a maximum matching M that contains e.
The matching problem can be generalized by assigning weights to edges in G and asking for a set M that produces a matching of maximum (minimum) total weight: this is the maximum weight matching problem. This problem can be solved by a combinatorial algorithm that uses the unweighted Edmonds's algorithm as a subroutine. [6]